Dealer Probabilities

For one reason or another, people like to know the math and probabilities in blackjack. Things like how often will the dealer bust or if the actions of your tablemates affects your win/loss outcome. So we thought we’d share the most common questions and answers below. Keep in mind that they won’t make you a better blackjack player. But they might reaffirm your beliefs in the strategies you use. If anything, they make for interesting facts to share with your friends or tablemates while playing.

How often will the dealer bust?

This will depend on a few different factors. One, the rules of the particular blackjack game you’re playing. Two, the number of decks in play. Three, the play from you and your opponents. Overall, though, any one factor will only increase/decrease the edge by a percent or two at most.

Here’s a general idea of how often the dealer will bust based on his up card.

• 2 – 35.3%
• 3 – 37.4%
• 4 – 39.6%
• 5 – 41.9%
• 6 – 42.3%
• 7 – 26.2%
• 8 – 24.3%
• 9 – 23%
• 10 – 21.3%
• A – 11.6%

The overall average is 28.2 percent. You’ll notice that the dealer is more likely to bust when he has a 5 or 6 than any other hand.

In fact, if you use basic strategy, you’re not expected to bust at all when the dealer shows a 4, 5 or 6, and you’re in terribly good shape when he shows a 2 or 3 (about 3 percent). But when the dealer shows a 7 or better your chances of busting are 20 percent or higher, or about 1 in every 4-5 hands.

How do the odds for the house change in different blackjack games?

There’s no way to get specific here, since there are countless variations for any one game, let alone from one game to the next. It’s a lot easier to understand why the odds change. Here is a list of rule variations that will affect the house edge:

• Number of decks. The more decks in play the better the edge for the dealer / house. That’s because more blackjacks are dealt with fewer decks. So the more decks, the fewer blackjacks, and the less 3:2 payouts the casino has to make. Players are also less likely to draw 10s in a double down situation.
• Dealer hits/stands on soft 17. When the dealer has to hit a soft 17 the house edge will decrease (in your favor). That’s because the dealer is more likely to bust or make a lesser hand that he has to hit (and possibly bust).
• Double down. When a player can double down at any time the house edge is decreased by .11%.
• Doubling after splitting. When players cannot double after splitting the house edge is increased by .14%.
• Resplitting. The fewer times you can split and/or you’re not allowed to split aces, the better the house edge is for the casino.
• Bonus / Side Bets. These have high payouts, but because the odds are so high this can add full percentage points to the house edge in favor of the casino.

You’ll notice that from one game to the next, in many cases, there is only a .2-.8 percent difference. It all has to do with the rules, and how you’re allowed to play your hands. The biggest differences will come with rules heavily in favor of the house (fewer splits, double downs, dealer stands on soft 17, etc) or games with side bets.

When does the dealer have the most advantage?

The dealer is less likely to bust with an ace, 10 or 9 point card showing. In terms of the game, they have the most advantage when there are more decks in play and if they’re able to stand on soft 17.

When does the dealer have the least advantage?

The dealer has the least advantage with a 5-6 showing. There are no (real) good cards that they can have in the hole. Nearly any card will give them a hand they have to hit, like a 14 or 16, that’s also vulnerable to busting to any 7-10 card.

Do the other players actions have a big effect on when the dealer busts?

Not as much as people would like to believe. Sure, you might have players that hit and hit, and therefore take away cards that would’ve otherwise busted the dealers. But for every player that does that, you have another player that doesn’t hit and gives those cards away. So it’s a wash.

In fact, the Wizard of Odds disproved this myth [Source: WOO: Multiple Decks]. He ran a simulation where two players followed basic strategy for over 1.6 billion hands. One had a loss of .289% and the other .288%.

On the second simulation the first player kept the same strategy, while the strategy of the 2nd player was altered. However, the first player was hardly affected with a loss of .282% over 1.05 billion hands. The second player had a loss percentage of 11.260%. So the actions from your opponents have very little impact on the probability of the dealer busting or making their hand.